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Gujarati JEE Mathematics : ગણ, સંબંધ અને વિધેય

Multiple Choice Questions

11.

f(x) = ax² + bx + c; x = 1, 2, 3 તથા g(x) = $open curly brackets table attributes columnalign left end attributes row cell bold 3 bold x bold space bold plus bold 1 bold semicolon bold space bold x bold space bold equals bold space bold 2 bold comma bold 3 end cell row cell bold space bold space bold space bold space bold space bold space bold space bold space bold 3 bold semicolon bold space bold x bold space bold equals bold space bold 1 end cell end table close$ હોય તેમજ બંને વિધેયો સમાન હોય, તો નીચેનામાંથી કયું સત્ય બને ?

a = b = c = 1
$straight a space equals space minus 1 half comma space straight b space equals space 11 over 2 comma space straight c space equals space minus 2$
$straight a space equals 11 over 2 comma space straight b space equals space minus 2 comma space straight c space equals 1 half$
$straight a space equals space 1 half comma space straight b space equals space 2 comma space straight c space equals space 11 over 2$

12. જો f(x) = cos (log x) હોય, તો f(x), f(y) - $bold minus bold 1 over bold 2 bold space open square brackets bold f open parentheses bold x over bold y close parentheses bold plus bold f bold left parenthesis bold xy bold right parenthesis close square brackets bold space bold equals bold space bold. bold. bold. bold. bold space bold.$

Tips: -

f(x) = cos (log x) હોય, તો f(y) = cos (log y)

$bold f open parentheses bold x over bold y close parentheses bold space bold equals bold space bold cos bold space open parentheses bold log bold x over bold y close parentheses bold space bold equals bold space bold cos bold space bold left parenthesis bold log bold space bold x bold space bold minus bold space bold log bold space bold y bold right parenthesis bold space$ તથા

$bold f bold left parenthesis bold xy bold right parenthesis bold space bold equals bold space bold cos bold space bold left parenthesis bold log bold space bold xy bold right parenthesis bold space bold equals bold space bold cos bold space bold left parenthesis bold log bold space bold x bold space bold plus bold space bold log bold space bold y bold right parenthesis$ મળે.

$bold f bold left parenthesis bold x bold right parenthesis bold space bold times bold space bold f bold left parenthesis bold y bold right parenthesis bold space bold minus bold space bold 1 over bold 2 bold space open square brackets bold f open parentheses bold x over bold y close parentheses bold space bold plus bold space bold f bold left parenthesis bold xy bold right parenthesis close square brackets bold equals bold space bold cos bold space bold left parenthesis bold log bold space bold x bold right parenthesis bold space bold times bold space bold cos bold space bold left parenthesis bold log bold space bold y bold right parenthesis bold space bold minus bold space bold 1 over bold 2 bold space bold left square bracket bold cos bold space bold left parenthesis bold log bold space bold x bold space bold minus bold space bold log bold space bold y bold right parenthesis bold space bold plus bold space bold cos bold space bold left parenthesis bold log bold space bold x bold space bold plus bold space bold log bold space bold y bold right parenthesis bold right square bracket bold equals bold space bold os bold space bold left parenthesis bold log bold space bold x bold right parenthesis bold space bold times bold space bold cos bold space bold left parenthesis bold log bold space bold y bold right parenthesis bold space bold minus bold space bold 1 over bold 2 bold space open square brackets bold 2 bold space bold cos bold space open parentheses fraction numerator bold log bold space bold x bold space bold minus bold space bold log bold space bold y bold space bold plus bold space bold log bold space bold x bold space bold plus bold space bold log bold space bold y over denominator bold 2 end fraction close parentheses bold space bold cos bold space open parentheses fraction numerator bold log bold space bold x bold space bold minus bold space bold log bold space bold y bold space bold minus bold space bold log bold space bold y over denominator bold 2 end fraction close parentheses close square brackets bold space bold equals bold space bold cos bold space bold left parenthesis bold log bold space bold x bold right parenthesis bold space bold times bold space bold cos bold space bold left parenthesis bold log bold space bold y bold right parenthesis bold space bold minus bold space bold 1 over bold 2 bold space bold left square bracket bold space bold 2 bold space bold cos bold space bold left parenthesis bold log bold space bold x bold right parenthesis bold space bold cos bold space bold left parenthesis bold minus bold log bold space bold y bold right parenthesis bold right square bracket bold equals bold space bold cos bold space bold left parenthesis bold log bold space bold x bold right parenthesis bold space bold cos bold space bold left parenthesis bold log bold space bold y bold right parenthesis bold space bold minus bold space bold cos bold space bold left parenthesis bold log bold space bold x bold right parenthesis bold space bold space bold cos bold space bold left parenthesis bold log bold space bold y bold right parenthesis bold space bold equals bold space bold 0 bold space$

13.

જો $bold f bold left parenthesis bold x bold right parenthesis bold space bold equals bold space fraction numerator bold x bold minus bold 3 over denominator bold x bold plus bold 1 end fraction bold comma bold space bold x bold space bold not equal to bold space bold minus bold 1$ હોય તો f⁽²⁰¹⁶⁾(2015) = ...... જ્યાં f⁽²⁰¹⁶⁾(x) એ f નું f સાથે 2016 વખત સંયોજિત વિધેય દર્શાવે છે.

2017
2014
2016
2015

14. જો P = {1, 2, 3, 4,} Q = {a, b, c, d} હોય તો નીચેનાં જોડકાં જોડો :

i - c, ii - a, iii - b
i - b, ii - c, ii - a
i - a, ii - b, iii - c
i - a, ii - c, iii - b

15.

જો f(x) એ દ્વિઘાત બહુપદી હોય તથા f(0) = 4 હોય તેમજ f(x+3) - f(x) 3x + 5, x હોય, તો તે દ્વિઘાત બહુપદી હોય.

3x² + x +24
x² + x + 24
$1 over 6$ (3x² + x + 24)
$1 half$ (x² + 2x + 9)

16. જો X = {4ⁿ - 3n - 1, n ∈ N} અને Y = {9 (n-1); n ∈ N} જ્યાં N = પ્રાકૃતિક સંખ્યાઓનો ગણ હોય તો X ∪ Y = ......... .

X
Y - X
Y
N

17. જો f(x)= $square root of bold log bold space bold left parenthesis bold sin bold space bold x bold right parenthesis end root$ હોય, તો વિધેય f નો મહત્તમ પ્રદેશ ......... હોય.

$left curly bracket left parenthesis 4 straight k space plus space 3 space right parenthesis space straight pi over 2 vertical line space straight k space element of space straight Z right curly bracket$
$left curly bracket space left parenthesis 4 straight k space minus 1 right parenthesis space straight pi over 2 vertical line space straight k space element of space straight Z right curly bracket$
$left curly bracket left parenthesis 4 straight k space plus space 1 right parenthesis space straight pi over 2 vertical line space straight k element of straight Z right curly bracket space$
$left curly bracket left parenthesis 4 straight k space plus space 3 space right parenthesis space straight pi over 4 vertical line space straight k space element of space straight Z right curly bracket$

18. f : (R -{-1} → R, f(x) = $fraction numerator bold 1 bold minus bold x over denominator bold 1 bold plus bold x end fraction$ હોય તો, $bold f bold space open parentheses fraction numerator bold x bold plus bold y over denominator bold 1 bold plus bold xy end fraction close parentheses$ = ..........

f(x) + f(y)
f(x)•f(y)
(f(x))²
f(x)/(f(y)

19. જો વિધેય f એ સમીકરણ $bold 3 over bold 10 bold space bold f bold left parenthesis bold x bold right parenthesis bold space bold plus bold space bold 2 over bold 10 bold f bold space open parentheses fraction numerator bold x bold plus bold 59 over denominator bold x bold minus bold 1 end fraction close parentheses bold space bold equals bold space bold x bold space bold plus bold space bold 3$ નું સમાધાન કરે (જ્યાં $bold x bold space bold not equal to bold 1$ ) તો f(21) .......

20. વાસ્તવિક વિધેય f(x) = $square root of bold x to the power of bold 2 bold space bold plus bold space bold 6 bold x bold space bold plus bold space bold 10 end root$ નો વિસ્તાર ...... મળે.

(-∞, 1)
[1, ∞]
R
(1, ∞)

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Gujarati JEE Mathematics : ગણ, સંબંધ અને વિધેય

Multiple Choice Questions

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